Search Documents

By R. L. Rickett, S. H. Kalin, J. T. Mackenzie

Aluminum killed low carbon steel, § which is now used extensively for severe deep drawing or other difficult forming operations, is unusual in that its grain structure, after cold reduction and box annealing in accordance with conventional continuous sheet or strip mill practice, often is elongated, although at times it is equiaxed. Since this unusual structure has been found superior for many, but not all, severe forming operations, recrystallization of the steel, both at constant temperature and on continuous heating, was investigated and compared with that of rimmed steel in the hope that something might be learned about the mechanism of, and the factors controlling, the formation of such elongated grains. In this structure, the grains are elongated both in the lengthwise direction of the strip and transverse to this direction, even though nearly all of the extension in both hot and cold rolling is in the lengthwise direction. The grains are thus roughly pancake-shaped, being longer and wider than they are thick, as observed also by Burns and McCabe,1 and as illustrated by the typical structures shown in Fig 1. Fig la, representing a conventional longitudinal section, shows the length and thickness of the grains, whereas Fig Ib shows their length and width as seen by examining a section parallel to the sheet surface. Both illustrate the very irregular grain boundaries usually associated with the elongated grain shape. A finer equiaxed grain structure in this same grade is shown in Fig Ic. Either the elongated or the equiaxed structure may be present in the annealed product, and in rare instances the two types may coexist in a single specimen, as shown in Fig 1 d. Isothermal Recrystalliza-tion of Rimmed and Alamimum Killed Steel An aluminum killed steel known to have an elongated grain structure after conventional processing (Steel B, Table l), was selected for the initial recrystallization studies; for comparison, a rimmed steel, A in Table 1, was used. Samples of each in the form of hot rolled strip 0.075 and 0.095 in. thick, respectively, were cold rolled on a small laboratory mill in steps of about 0.010 in. per pass to obtain total reductions of 40 and 60 pct. Small pieces of the cold reduced strip were heated in lead at selected constant temperatures for one of several periods of time, then cooled in air. Rate of heating in the lead was, of course, very fast. Hardness of the cooled specimen was measured and a longitudinal section examined metallographically. Isothermal recrystallization curves for these two steels at 1050°F, based on hardness of the air cooled specimens, are shown in Fig 2 in which the amount of recrystallization corresponding to each plotted point is indicated. The marked difference in the behavior of these two types of steel is evident. After a corresponding amount of cold reduction, the rimmed steel recrys-tallizes in a much shorter time than the killed steel and the shape of its recrystallization curve, (plotted on a logarithmic time scale), is very different. The curve for rimmed steel indicates that recrystallization is analogous to isothermal transformation of aus-i.enite in that it proceeds at a progressively faster rate up to some 50 pct recrystallization, then at an increasingly slower rate. For the aluminum killed steel, however, the start of

Jan 1, 1950

By N. J. Grant, B. C. Giessen, R. Koch

The system Nh-Ir was investigated over the complete concentration range by metallography and X-my techniques, using forty one alloys. The solubility limits of terminal and intermediate phases and the solidus temperatures were determined. Five intermediate phases were found: a Nb3Ir, cubic, Cr3O type; tetragonal, ofecr thorhomhic, isostruc-turn1 with (ta-Rh); and a Nhlr3. cubic, AuCu, type. a Nb3lr and a Nbfr3 melt congruently; three eutectic and three pentectic reactions occur. The phase diagram of the Nb-Ir system had not been fully treated in the literature; only surveys of intermediate phases were found.1"5 In this study, the details of the phase boundaries were investigated as well as the crystallography of the intermediate phases. EXPERIMENTAL METHODS The experimental procedures such as arc melting of powder compacts, heat treatments, solidus measurements, X-ray, and metallographic observation were identical with those used in the work on the Nb-Rh phase diagram.&apos; They will therefore not be repeated here except where the conditions differed. The purity of the niobium powder was as stated in Ref. 6; the iridium powder of 99.9+ pct purity from J. Bishop and Co., Malvern, Penn., did not contain impurities exceeding 100 ppm, except rhodium (200 ppm). The melting points and vapor pressures of both elements are very similar. This fact contributed to a very small weight loss on melting and facilitated preparation of homogeneous alloys. As shown in Ref. 6 for Nb-Rh, no oxygen pick-up exceeding 200 ppm had to be considered; this was regarded as valid also for Nb-Ir. A total of forty one alloys were used in the determination of the phase diagram; their concentrations are shown in Fig. l, which presents the phase diagram. The concentration limits as determined by the weight-loss method averaged <0.2 at. pct, and never exceeded 0.5 at. pct. Heat treatments were carried out as described in Ref. 6. Depending on the concentration, only tantalum, tungsten, or iridium containers were employed, avoiding oxide crucibles altogether. Alloys from 0 to 25 and from 65 to 100 at. pct Ir were homogenized at 2095°C for 15 hr, intermediate compositions from 25 to 65 at. pct Ir for 65 hr at 1780°C. A typical annealing-time schedule is presented in Table I. Solidus points were measured as described in Ref. 6 with the modification that samples rich in niobium were held between pieces of tantalum foil and samples of high iridium concentrations were held between rhenium platelets or in iridium wire. After each run it was ascertained metallographically that no reaction with the holder had occurred. Rhenium was selected as holder material after it had been shown in separate tests that the melting points of Re-Ir alloys rise continuously from 2440°C. Metallographic examination was carried out as described in Ref. 6, and the same procedure and etchants were used successfully. While metallographic discrimination between a Nb3lr and o was easily possible, X-ray diffraction was necessary to separate al and ct2. X-ray powder patterns were taken and evaluated as for Nb-Rh6 yielding the error limits indicated in Table 111, to be introduced later. For the determination of the invariant reactions and phase boundaries, the same techniques as for Nb-Rh6 applied. The general accuracy of invariant concentrations is regarded as somewhat higher than for Nb-Rh due to the small slope of most solvus lines.

Jan 1, 1964

By Paul J. Bennett, James E. Castle

The sillimanite family of minerals, including kyanite, sillimanite, and andalusite, are anhydrous aluminum silicates with the formula A12O3-SiO2. Dumortierite and topaz are also included in this group because they are closely allied in composition and thermal behavior. However, neither are mined commercially today. They are typical metamorphic minerals which are found in metamorphic rocks on every continent. Sillimanite minerals are prized chiefly for their refractoriness and are important components in a broad range of acid refractory products, especially in mortars and castables. World production of sillimanite minerals is currently about 400,000 tpy and has been increasing at the rate of 3 to 8% a year for many years (Anon., 1972). While these minerals have widespread occurrence, the consumption of sillimanite minerals is concentrated in the relatively few highly industrialized areas where refractories are manufactured, and which in turn are typically close to the major iron and steel producing regions of the world. Thus northern Europe,. England, the United States, and Japan are the principal consumers of refractories and sillimanite minerals. Of these countries only the US is a significant producer. Uses of Kyanite The following specifications are typical for the domestic kyanite industry: Raw Kyanite Concentrates Chemical Analysis 56% AI2O3 min 0.1% CaO max 42% SiO2 0.1% MgO max 1% Acid soluble 0.3% combined Fe2O3 alkali max 1.2% TiO2 max Available Sizes 35, 48, 100, 200, and 325 mesh The largest use for domestic kyanite, both raw and calcined, is in the manufacture of refractory mortars, cements, castables, and plastic ramming mixes. In these applications kyanite constitutes from 10 to 40% of the mixture, the balance being refractory clays and coarser grog materials. A certain proportion of raw kyanite is used to offset the shrinking of the clay binder, whereas the calcined kyanite is used in the coarser sizes for body. Certain high grade refractory shapes and kiln furniture are composed chiefly of graded sizes of calcined kyanite bonded with a little ball clay. In most applications, however, kyanite is used only to fortify the mix or as a minor ingredient. Some manufacturers of mullite brick use domestic calcined kyanite for the fine-grained portion of the brick, but seldom in quantities exceeding 10% by weight. Kyanite is used by ceramic manufacturers of wall tile and sanitary ware to offset shrinkage and cracking after firing. Indian kyanite has traditionally been used to make the coarse grog sizes needed for the manufacture of mullite brick, and for the grog portions of mortar, cement, and castable mixes. It has been largely replaced, however, by synthetic mullite, high fired flint, and diaspore clay or calcined bauxite for other applications. Indian kyanite has been available in lump as well as in granules and concentrates, as are sillimanite materials from India and South Africa. Andalusite is available as 8 mesh granules and as fines with chemical analyses not unlike those of domestic kyanites. From time to time and from place to place minor amounts of other aluminum silicate minerals such as dumortierite, topaz, and pyrophyllite have been made available at various prices and specifications, but have not been significant factors in the refractory industry. A mixture of kyanite and sillimanite of relatively fine grain-size and of low iron content was at one time offered to the molding sand industry by the Du Pont Co. as a byproduct from their deposits of heavy

Jan 1, 1983

By Oscar M. Wicken

The mineral magnesite (MgCO3) if pure would consist of 47.7 pct MgO and 52.3 pct CO2. It is one of the calcite group of rhombohedral carbonates which includes calcite (CaCO3), siderite (FeCO3), rhodocrosite (MnCO3), and smithsonite (ZnCO3) among others. The members of this group enter into a wide range of substitutional solid solutions, whose range is still imperfectly known.* MgCO3 and FeCO3 appear to form a complete series of which breunnerite (ferroan magnesite) is a well known variety. Because of the considerable difference in size of the Ca and Mg ions, there is only a limited range in substitution in the MgCO3-CaCO3 series. (Dolomite, not strictly a member of the calcite group, may be regarded as an ordered structure developed when Ca: Mg is approximately 1:1.) The practical consequence of these relationships is that the lime carbonates (calcite and dolomite) are commonly present in magnesite deposits chiefly as mechanical mixtures. Magnesite may be either crystalline or "amorphous" (cryptocrystalline). The crystalline form has a hardness of 3.5 to 4.0. The color may range from white to black through shades of yellow, blue, red or gray. It is rarely found pure but generally contains variable amounts of iron, lime, and silicate minerals. Color cannot be used as an index of purity except under specific local conditions in a single quarry. In a given quarry an experienced man may be able roughly to grade magnesite by intuitively assessing such features as crystallinity and color. Crystalline magnesite occurs in larger deposits, but the cryptocrystalline variety is more common. The latter is fine-grained and compact and shows no cleavage; often it is descriptively called "bone magnesite." The fracture is usually conchoidal, and hardness is 3.5 to 5.0. It is normally white, but sometimes it is light yellow to orange or buff because of included impurities. In addition to lime and iron, which may be present in small amounts, silica may be present as inclusions of serpentine, quartz, chalcedony, or other minerals. In general, commercial deposits of "amorphous" magnesite have lesser amounts of accessory minerals than does crystalline magnesite. The specific gravity of "amorphous" magnesite is 2.90 to 3.0. Pure, crystalline magnesite has a specific gravity of 3.02, but iron carbonate, commonly present, raises the specific gravity to somewhat higher values. Magnesite dissociates, when sufficiently heated, into magnesia (MgO) and carbon dioxide. Either simultaneously or upon further heating the magnesia develops a crystalline structure identical with that of the natural mineral, periclase, which occurs sparingly in nature but not normally in workable deposits. Brucite is another magnesium mineral capable of being directly reduced to magnesia by heat alone. Brucite (Mg(OH)2) has been mined for the production of various grades of magnesia. It theoretically contains 69.1 pct MgO and 30.9 pct H2O. It may be white, but is generally blue or green with a gray cast. It has a translucent appearance. The mineral is soft (hardness, 2.5), and has a specific gravity of about 2.4. Nomenclature of Products The word "magnesite" literally refers to the natural mineral, but common usage has applied it plus a prefatory word to two other

Jan 1, 1960

By R. T. Hukki

This paper presents a preliminary analysis of the fundamental relationship between the net energy used and the respective product size throughout the entire range of sizes covered by crushing and grinding, and an attempt to find a sensible correlation between the existing theories. Walker, Lewis, McAdams, and Gilliland&apos; have given the following differential equation of a general form for comminution: dE = -C§ [1] where E is the net energy required per unit weight in a certain process of comminution; x is the factor indicating the fineness of the product; n is the exponent indicating the order of the process, and C is a constant related with the material, units chosen, etc. H exponent n in the above equation is replaced by numerical figures 2, 1, and 1 1/2, the integrated form of the general equation leads to the well known fundamental theories represented by the law of von Rittinger,&apos; law of Kick, and the third theory of comminution by Bond, respectively. The total net energies (E) from infinite feed size to a product of size x are as follows: The net energy required in a certain process of comminution is proportional to the new surface developed according to the law of von Rittinger, to the weight or size of the bodies treated according to the law of Kick, and to the length of the new cracks formed which initiate breakage according to the theory and explanation by Bond. On a logarithmic paper, where particle size is presented on the abscissa and energy consumption on the ordinate (see Fig. 21, all three relationships are represented by straight lines. The slope m of the line according to the law of von Rittinger is equal to -1.0; of Kick, 0; and of Bond, -0.5. Experimental evidence in favor of the law of Rittinger has been presented, e.g., by Gross and zimmerley5 on quartz crushed in a drop weight crusher and evaluated for surface by the method of dissolution, by Dean on magnetite crushed by a similar method and evaluated for surface by the determination of coersive force, by piret7 and co-workers on a group of minerals crushed again by a similar method as well as by compression and evaluated for surface by permeability and gas adsorption methods, and by schellinger8 on a group of minerals ground in a calorimetric ball mill and evaluated for surface by gas adsorption. Experimental evidence in favor of the law of Kick seems to be scant in the field of comminution. On the other hand, in the field of mechanical engineering Kick&apos;s law seems to be of fundamental nature in processes such as cutting, pressing, shaping, and rolling of metallic substances. Experimental evidence in favor of the third theory has been provided by Bond." To a large extent, data are based on the vast amount of grindability tests performed in the laboratories of Allis-Chalmers Manufacturing Co. In addition to the devoted proponents of one or the other of the basic theories listed above, certain investigators have indicated that one of the theories might be applied for a certain range of sizes, while another theory might be used for other sizes. In a discussion of a paper by Bond," Dobie" presented a statement at the International Mineral Dressing Congress in London (1952) indicating that 1) for large particles, the law of Kick was approximately correct; 2) for finer particles, von Rittinger&apos;s suggestion was nearer to the truth; and 3) Bond&apos;s new

Jan 1, 1961

By H. Warlimont

Precipitation of cementite plates from carbon-rich austenite gives rise to localized formation of martensite in the matrix next to the precipitate upon quenching. The growth of this martensite is urmsually restricted. A distinct lattice relationship is found between this martensite and the cementite phase. It is concluded that the martensite is nacleated in the region of lowest carbon concentration at the austenite-cementite integace, with low-energy matching to the cementite lattice. The restriction of the growth of the martensite phase to the vicinity of the cementite plates can be explained by misfit in the austenite -martensite glissile interface and the uphill carbon gradient in the austenite. The investigation was carried out by light- and electron-microscopy and by electron-diffraction of thin foils. THE precipitation of cementite from carbon-rich austenite gives rise to a localized formation of martensite in the matrix next to the precipitate upon quenching. This behavior has been described previously by A. B. Greninger and A. R. Troiano1 for a 1.78 pct C steel ("pseudomorphic martensite"), and by A. Hultgren2 for a Fe-0.99 pct C—5.20 pct Mn steel. By measuring the axial ratio of the martensite phase,&apos; it was found that the carbon content of this martensite was lower than that of the martensite which formed without prior partial transformation to cementite. Therefore, it was concluded that lowering of the carbon concentration in the matrix next to the precipitate raised the M, temperature locally and thus led to nucleation of martensite at the ce-mentite-austenite interface. However, the restriction of the growth of the martensite phase to the vicinity of the cementite plates cannot be explained by localized carbon impoverishment alone. Under ordinary conditions a martensite plate which has been nucleated in a favorable site can continue to grow until it encounters a physical barrier, or until it encounters a compositional barrier in the matrix, where the total free-energy change for the reaction is not negative, since it has been shown by numerous experiments that the activation energy for growth of ordinary martensite is virtually zero.&apos; An investigation was conducted by transmission electron microscopy and electron diffraction to study this extraordinary martensite. It was expected that crystallographic in addition to compo- sitional conditions caused this abnormal mode of martensite formation. MATERIAL AND PROCEDURE An Fe-C-Mn alloy containing 1.15 pct C and 5.1 pct Mn was used for most of the experiments. For metallographic work, specimens 15 by 15 by 3 mm were used. For preparation of thin films, the initial specimen size was 15 by 15 by 0.7 mm. The heat treatment of each specimen consisted of austenitizing for 1/2hr at 1100&apos;~ in an argon atmosphere, subsequent isothermal holding in a lead bath at one of a series of different temperatures, and, finally, quenching into brine at room temperature. For metallographic examination, the specimens were mounted in bakelite (slight tempering effects resulted from the heat in the mounting press) ground, polished, and etched in nital. Thin films for transmission electron microscopy and electron diffraction were obtained by grinding the specimens to approximately 0.2 mm thickness and subsequent electrolytical thinning. The orientation relationships were evaluated from sets of electron micrographs and selected-area electron diffraction patterns of single units of the transformation products and the adjacent matrix. RESULTS In the alloy which was used for the experiments, proeutectoid carbide precipitates over a wide tem-

Jan 1, 1962

By Charles Law McCabe, Lyndon H. Everett, Edna A. Dancy

It has been found that the carbide phase present at equilibrium in the system M-H2-CH4, at about 600°C, is MC for the rare-earth metals Ce and Pr. X-ray diffraction analysis showed that the monocarbides have fcc structures with lattice constants of 5.036 + 0.009Å and 5.131 + 0.001Å for CeC and PrC respectively. Gaseous equilibrium measurements were used to calculate the standard free energy of formation of the monocarbides from the elements. for the formation of (+ 1300) for the formation of PrC. THE rare-earthdicarbides, and their crystal structures, have been known for some years,l but only more recently were the carbides CeC,2,3 Ce2C3 2 and CeCS3 reported. In 1958 to 1959, Spedding et al. published work on the lanthanum-carbon system4 and other rare-earth metal-carbon systems,5 proving the existence of M2C3 and MC2, and measuring the lattice constants. They also demonstrated that tri-rare earth carbides, M3C, exist for the rare-earth metals samarium through ytterbium. However, they concluded that the cerium monocarbide reported by Brewer and Krikorian2 and by Warf,3 and given a fcc structure with a lattice constant of 5.130Å bythe former workers, was, in fact, cerium metal with carbon dissolved in it. They were also unable to find any evidence for the existence of Warf&apos;s CeC3, for which no structural details had been given. Even more recently, Palenik22 reported the existence of only M2C3 and MC2, having been unable to find any evidence for the existence of any other rare-earth carbides. There are no published experimentally derived thermodynamic data for the formation of any of these carbides, although Brewer and Krikorian6 have estimated values of for CeC, Ce2C3 and CeC2. The objective of the present investigation was; to determine experimentally the free energy of formation of any of the reported carbides of cerium and praseodymium, through a study of the rare-earth metal-hydrogen equilibrium. EXPERIMENTAL A methane-hydrogen mixture was circulated, in a closed system over previously prepared cerium or praseodymium hydride, and when equilibrium had been attained, the gas mixture was analyzed by selectively oxidizing the hydrogen and condensing out the water formed. The metal hydrides were used as starting material for convenience because, otherwise, the hydrogen in the gas mixture would immediately dissolve in the metals; in addition, the metals would not react with methane alone at the experimental temperature (around 600°C). The circulating system was based on that used by Browning, DeWitt, and Emmett7 for similar studies on iron carbides. It consisted of a quartz reaction vessel, all-glass circulating pump, analysis tube containing copper oxide that could be heated to 300" C by means of a small furnace, a solid CO2-methanol trap, and a double limb absolute manometer, Fig. 1. A cathetometer, capable of reading to 0.005 cm, was used to measure the difference in height between the two columns of mercury. In its final form, the reaction vessel was enclosed in an outer jacket, containing approximately the same pressure of hydrogen as that within, to reduce errors due to diffusion of hydrogen out through the fused silica of the reaction vessel., The circulating system was supplied with

Jan 1, 1962

By Joseph Daniels

IN connection with a study of the feasibility of establishing a blast-furnace industry in the Puget Sound region of Washington, possible sources of ore supplies along the Pacific rim were investigated. Many of the South American countries are known to contain important resources of iron, particularly Brazil and Chile. This latter country, because of its position on the west coast and the easy accessibility of its de- posits, appeared to be a logical place to consider as a potential supply for the Pacific Northwest. Accordingly, a brief field study was made of the deposits in September, 1924. Attention was confined to a limited number of properties on the west coast in the provinces of Antofagasta, Atacama, and Coquimbo. Passing consideration was given to the question of coal resources, and a short visit was made to a blast-funace plant at Corral in southern Chile which had been operated for a limited period as a producer of pig iron. In the following paper, a brief outline is given of the general observations made and of the salient facts rioted in the time available for the general study.

Jan 1, 1926

By W. D. Robertson, A. S. Tetelman

The technique of decorating dislocations was employed to investigate deformation and fracture resulting from Precipitation of hydrogen in Fe-3 pet Si single crystals. It is shown that cracks are produced on (100) planes inside crystals, as a consequence of the precipitation of hydrogen gas, either when crystals are quenched from a hydrogen atmosphere at elevated temperatures or cathodically charged with hydrogen at room temperature. Plastic deformation in the vicinity of cracks, observed as arrays of decorated dislocations, is in conformity with the calculated stress distribution about a crack containing an internal pressure, and the observations provide information permitting a detailed analysis of the mechanics of crack growth. The fracture characteristics of crystals containing internal cracks were evaluated at 25o and -196°C and the results are related to the mechanism of hydrogen embrittlement in terms of the growth of preexisting cracks. HYDROGEN in bee iron or steel produces two characteristic changes in mechanical properties: I), a decrease in ductility (macroscopic strain at fracture) that depends on temperature and strain rate, and 2), spontaneous fracture under static load that depends on time and apparent stress. Resolution of these phenomena into the microscopic processes that combine to produce the macroscopic effects is especially difficult in the Fe-H system in which the active component cannot be directly observed and only maintained in equilibrium with great difficulty in the temperature and pressure range in which embrittlement phenomena appear. As a result of these complications, verification of the numerous hypotheses&apos;-5 that have been proposed to explain the microscopic mechanism of embrittlement depends on self-consistency with measured changes in macroscopic properties that are averaged over the volume of a specimen. It is obviously important to obtain a more direct evaluation of the microscopic processes that combine to produce embrittlement. Accordingly, the present investigation was designed to identify and observe, as directly as possible, the microscopic effects of introducting hydrogen into a bee crystal. It was concluded from a previous investigation6 of X-ray line broadening, produced by introducing hydrogen into pure iron at room temperature, that the only effect that could be associated with the introduction of hydrogen was plastic deformation; in particular, dilation of the lattice was not observed, within ± 0.01 pet, and no evidence was found that could be interpreted to support the idea7&apos;* that hydrogen occupies tetrahedral interstitial sites in the iron lattice. The absence of lattice dilation is consistent with the extremely small solubility of hydrogen in bee iron9,10 (0.015 at. pet at 900oC and 1 atm pressure), and the evidence of plastic deformation is consistent with the fact that hydrogen, introduced by cathodic charging, eliminates the carbon yield point.11-13 Following this investigation, the immediate problem was to devise a method by which plastic deformation could be observed directly. The technique employed by Hibbard and Dunn14 to observe the movement of dislocations during bending and subsequent polygonization of Fe-3 pet Si single crystals was adopted and modified for the present purpose to include the observation of dislocation arrays in the volume of the crystal, and their association with the fracture process. EXPERIMENTAL PROCEDURE Single crystals of a high purity Fe-3 pet Si alloy, containing 0.007 pet C, were grown in vacuum by

Jan 1, 1962

By N. S. Bornstein, M. A. DeCrescente

ThE nickel and cobalt base superalloys employed in gas turbine engines under some conditions&apos; oxidize at an accelerated rate when exposed at elevated temperatures to atmospheres containing minor quantities of sea salt. It is generally agreed by investigators in the field that the major steps comprising this phenomena of accelerated oxidation, also called hot corrosion or more commonly, sulfidation, are a) a slag composed primarily of Na2S04 is formed on turbine components, b) the protective oxide scale is rendered ineffectual, c) the slag reacts with. the substrate to form metal sulfides, and d) the substrate is rapidly oxidized. Sodium sulfate, a minor constituent of sea salt, is formed within the gas turbine engine from the reactions between NaC1, the major constituent of sea salt, and the oxides of sulfur.&apos; Depending upon concentration, engine compression ratio, and temperature, the Na2S04 will be present in the gaseous or condensed state. It has been determined that in order for sulfi-dation to occur the Na2S04 must be present in the condensed state.&apos; Although a number of sulfidation mechanisms have been postulated, there is no consistent explanation of oxide scale breakdown and subsequent catastrophic oxidation. Some investigators believe that after oxide scale breakdown, the Na2SO4 reacts with the substrate to form lower-valent sulfur compounds. The accelerated rate of oxidation is due to oxidation of a nickel-sulfide phase." Other investigators believe that sulfur from the fused salt reacts with chromium in the alloy to form chromium-rich sulfides; thereby depleting the alloy of an element which imparts oxidation resistance.3,4 This publication will demonstrate that the accelerated rate of oxidation associated with sul-fidation is due to interactions between Na20, a con-stituent of NazSO.,, ancl the substrate. The aim of this study was to separate and determine the effect of compounds of sulfur and sodium on the oxidation kinetics of various nickel-base superalloys, in order to elucidate the sulfidation mechanism. The work reported herein is sponsored in part by the Naval Ship and Development Center-Investigation of EXPERIMENTAL PROCEDURE The nickel base alloys B-1900, U-700, and Waspaloy were chosen for this study. The nominal compositions are presented in Table I. The specimens, approximately 1 in. by 1 in. by 0.060 in. received in the "as cast" condition were polished with 600 grit emery, washed, and rinsed with acetone immediately prior to oxidation experiments. Sulfida-tion attack was duplicated in the laboratory by apply-ing a saturated aqueous solution of Na2S04 onto the al loy substrate and subsequently exposing the specimens in oxygen at elevated temperature. The method of Na2S04 application is described elsewhere in detail.6 In another set of experiments the affected substrate microstructure associated with sulfidation was reproduced free of the normal oxide scale, by reacting and diffusing elemental sulfur into the alloy. The experimental procedure is also described elsewhere in detail. All oxidation studies were performed using an Ainsworth thermobalance type RV-AU-1, which is readable to 0.01 mg and is reproducible to ±0.03 mg. The specimens, introduced into a heated furnace, were exposed in the temperature range 800" to 1000°C

Jan 1, 1970

By J. R. Morison, M. P. O’Brein, J. W. Johnson, S. A. Schaaf

The force exerted by unbroken surface waves on a cylindrical object, such as a pile, which extends from the bottom upward above the wave crest, is made up of two components, namely: 1. A drag force proportional to the square of the velocity which may be represented by a drag coefficient having substantially the same value as for steady flow, and 2. A virtual mass force proportional to the horizontal component of the accelerative force exerted on the mass of water displaced by the pile. These relationships follow directly from wave theory and have been confirmed by measurements in the Fluid Mechanics Laboratory of the University of California, Berkeley. The maximum force exerted by breakers or incipient breakers is impulsive in nature, reaching a value much greater than that produced by unbroken waves but enduring for only a short time interval. This impulsive force represents the ultimate development of the accelerative force and is produced by the steep wave front and large horizontal acceleration at the front of a breaker. This impulsive force greatly exceed. the drag force computed from the particle velocities of the breaker. The reader is cautioned that these preliminary results are applicable only to single piles without bracing and are likely to be modified somewhat where multiple piles are driven, one within the influence of the other or where multiple piles are connected by submerged bracing. This paper is essentially a preliminary report submitted at this time because of the current importance of wave forces in the design of offshore structures. An extended series of additional experiments is planned for the near future. Theoretical Relationships For the sake of simplicity of treatment, the theory will be developed from the equations for waves of small amplitude. The horizontal displacement of a water particle is described by the equation 2p cosh — (d + z) H L 2pt X =----------------------sin ----- . , (1) 2 2pD T sinh------ L The horizontal component of the orbital velocity is obtained by differentiation with respect to time as 2p cosh — (d + z) pH L 2pt u = ------------------- cos— .... (2) sinh- L The acceleration of the water particles at any position is obtained by again differentiating with respect to time as 2p cosh — (d + z) 9 u -2vH L 2pt -----=----------------------------sin ----- . . (3) 3 t T2 2pd T sinh------ L where H = wave height — ft L = wave length — ft d = still water depth — ft z = depth below the still water measured negatively downward — ft. T = wave period — sec t = time — sec The force exerted on a differential section, dz, in length is pD2 s u pD 1 dF= [CM (p/4) st + Cn/2 u2] dz • • (4) where D = pile diameter — ft p = water mass density — slugs/ft3 C, = coefficient of mass C,, = coefficient of drag Substituting for a s u/s t arid u2 from Eqs. (3) and (2), the force per unit length at any position z is dF p2 pD H2 &apos; / = — [- fM sin ? ± fD cos2 ? ] . . . (5) dz 2T2 fM D fD 2pt Cm = pA/H:CD = A2;? = T [+ cos2 ? for 0 < ? < p/2 cosh— (d+z) 3p L — < o < 2p Sin L -cos2 ? for p/2 <? <3p/2 The sin 9 term (inertia) i- negative for 0 < 0 < p and positive for p < ? < 2p. Values of A and A&apos; appear in Fig. 1

Jan 1, 1950

By M. J. Spendlove, H. W. St. Clair

An automatic surface-follower mechanism was used to measure the surface temperature and the rate of evaporation of molten zinc while undergoing distillation at low pressure. At pressures of 50 to 100 microns Hg, the rate of evaporation may be 60 to 80 pct of the theoretical maximum corresponding to the measured temperature. The rate decreases rapidly at pressures above 100 microns Hg, to only 7 pct of the theoretical maximum at 2000 microns Hg. Measured temperature gradients at the surface are in agreement with theoretical gradients calculated from the heat of vaporization, rate of evaporation, and thermal conductivity of molten zinc. THIS paper covers a series of careful measurements of the rate of evaporation of molten zinc at low pressures, undertaken as a part of a general investigation on the separation of metals by distillation.&apos; Preliminary results on the rate of evaporation of zinc were described in a previous publication.&apos; The results of the preliminary study are as follows: 1—The observed rates of evaporation of zinc were as high as 0.60 g per sq cm per min, corresponding to 75 pct of the maximum rate as determined by the temperature of the metal. 2—The evaporation rate was decreased from 0.30 g per sq cm per min at a pressure of 25 microns to only 0.09 g per sq cm per min when the pressure was increased to 5 mm. 3—The temperature of the surface during rapid evaporation may be 35" to 100°C less than the main mass of metal. Observed temperature gradients at the surface are consistent with those calculated from the heat of vaporization and the thermal conductivity of liquid zinc. In the preliminary experiments, the rate of evaporation was determined from the loss in weight of the metal in the crucible during the test. This was compared with the weight of the condensate. Obviously, this method was subject to error because of some uncertainty as to the period of evaporation that should correspond to the loss in weight. Furthermore, this method did not permit taking into account probable variations in the rate of evaporation during the test. A more serious shortcoming was that the temperature at the evaporating surface was not known, so the maximum theoretical rate of evaporation could not be calculated accurately. To improve the precision of rate measurements and to allow accurate measurements of the surface temperature, a refined experimental technique was developed whereby the temperature and position of the surface could be measured accurately. This was done by an automatic surface-follower mechanism that gave a continuous record of the surface temperature and the amount of zinc evaporated. These data permitted an instantaneous determination of the actual rate of evaporation and the surface temperature throughout the test. Pure zinc (99.99 pct Zn) was used in all experiments. Description of Distillation Furnace The details of construction of the distillation furnace are shown in Fig. l. The furnace is enclosed in a large quartz tube open at one end. The open end of the quartz tube is sealed by means of a water-cooled head. The entire enclosure is vacuum tight. The connection between the water-cooled head and the quartz tube is sealed by means of a rubber gasket which fits tightly against the smooth end of the tube. The metal is heated by induced current set up in the molten zinc and the walls of the graphite crucible by means of a water-cooled induction coil outside the quartz tube. High frequency current is passed through the induction coil from a 6 kw mer-

Jan 1, 1952

By Klaus M. Zeitler

INTRODUCTION One cannot discuss the subject of "Raising Capital in the 1990s" without having a crystal ball and a reliable fortune teller. This discusses "Raising Capital for the 1990sW, which is what Metal1 Mining Corporation did in 1987. We raised (3166 million in an IPO (initial public offering) that was originally planned for only some (375 million. Why did we raise this money? How did we do it, and why was this IPO so successful? The answer to the first question requires a description of the promoter and principal shareholder of Metal1 Mining Corporation, Metallgesellschaft AG. This West Germany company was founded over 100 years ago in Frankfurt as a trading house for non-ferrous metals. It has developed into one of the world&apos;s leading firms in the non-ferrous metals industry. The company&apos;s worldwide activities in all areas of that business include mining, smelting and refining, the trading of ore, base and precious metals, the production of semi-fabricated and finished metal products, and the provision of engineering, construction and transportation services. Metallgesellschaft AG has also diversified into many other areas, the most significant of which are manufacturing, the production of chemicals, the development and application of technical and chemical processes, the planning and construction of industrial plants, and activities associated with finance, insurance, shipping and freight forwarding, and the provision of barter and countertrade services. The company maintains a network of more than 100 offices around the world; it employs some 25,000 people in its worldwide activities. [Selected financial data, as of September 30, 1987: (MetaUgesellschafl AG) Working Capital DM 8%.6 million CDNS 672.8 million Long Term Debt DM 568.0 million CDNS 426.2 million Sales DM 14.9 billion CDNS 11.2 billion Net Income DM 87.7 million CDN$ 65.8 million Market Capitalization at April 27, 1987: (Metallgesellschafi AG) Outstanding Shares ~,6oo,o0o DM 1,875 million CDNS 1,407 million] For the fiscal year ended September 30, 1987, Metallgesellschaft AG had, on a consolidated basis, net sales of DM13.3 billion, net income of DM100 million and total assets of about DM7.0 billion. Metallgesellschaft AG established the American Metal Company, a predecessor of AMAX Inc. one of the largest ventures undertaken by Metallgesellschaft AG then was the acquisition, through the American Metal Company, of a majority share in the Mexican Penoles mine, a large lead and silver deposit. METALLGESELLSCHAFT AG Figure 1 depicts an overview of Metallgesellschaft AG before and at the time the initial public offering of Metall Mining Corporation&apos;s shares took place. It shows that mining was far from the centre of Metallgesellschaft&apos;s activities. Therefore, it could not expect to receive an extraordinary amount of board attention. Thus, mining investments not only had to compare well with other mining opportunities, but were in fierce competition with projects from other divisions. In addition, mining was sub-divided into two separate departments -- domestic and international. These two departments had different management styles and diverging interests which resulted in a minimum co-operation between them. The domestic mining department was primarily interested in the survival of the local mines. These mines were characterized by rising operating costs and declining ore grades. It took a special commitment and continued ingenuity to develop and adjust to local conditions, and modern mining and processing technology, in order to remain competitive, or at least survive within the international mining industry. Local management

Jan 1, 1990

By E. O. Wagner, V. F. Parry, J. B. Goodman

The low-rank coals containing 10 to 50 pct natural bed moisture represent over half of the tonnage reserve of the available solid fuels of the United States, but only about 2 pct of United States coal production is derived from these fuels. Increased utilization of these large reserves will result if the bed moisture can be removed at the mine in high-speed low-cost processes. This paper presents a theoretical and experimental study of the factors affecting high-speed drying of coal dusts. The time required to heat particles of coal is proportional to the square of their diameter, and it is calculated that the probable time in minutes is equal to 6D2. In other words, a 1/16 in. coal particle should be heated to drying temperature in 1.5 to 2.0 sec. Likewise, 1/8 in. particles should be heated in about 6 sec. The net heat required to dry subbituminous coal and lignite varies from 240 to 375 Btu per pound, depending upon the moisture removed, and this heat can be obtained from 42 to 61 cu ft of hot gases at 600°F. The necessary heat also can be obtained from 7.5 to 11 cu ft of gas at 2000°F. A description of the design and operation of a pilot plant for flash drying coal dusts is presented. This plant dries 1/16 in. by 0 coal dust in suspension in 1.5 to 2 sec with 600°F gas at a rate of 1300 lb per hour per square foot of column area and operates continuously at an efficiency of about 85 pct. The design and operation of another pilot plant for drying 1/8 in. by 0 coal dusts Is also described. This unit dries coal in the fluidized state using the sensible heat of gases introduced at 2000°F and processes coal at a rate of about 1500 Ib per hour per square foot of grate area at 85 to 90 pct efficiency. Over 90 pct of the bed moisture of low-rank coal dusts can be removed by the methods described. The heating value of lignite can be increased 45 pet and that if subbituminous coal 25 pct in a few seconds. The physical and chemical properties of coal dusts before and after drying are presented in the report, and it is shown that the bulk density of the dried coal is equal to that of the raw coal. This phenomenon makes it possible to ship 25 to 45 pct more heat in a railroad car with consequent savings in freight costs. Introduction For several years the Subbituminous Coal and Lignite Section of the Coal Branch of the Bureau of Mines at Golden, Colo., has been concerned with upgrading low-rank coals by removal of natural bed moisture. These fuels contain 10 to 50 pct total moisture, which reduces their industrial value considerably. In 1938, investigations were initiated in cooperation with the University of North Dakota to study drying of lignite by the Fleissner process with heat derived from high-pressure saturated steam. Two pilot plants were built, and two reports were published giving the results of this work.l,2 It was demonstrated that lump lignite and subbituminous coal

Jan 1, 1950

By John P. Huger

me phase diagram for the system Ag-Si has been established by thermal analysis. The diagram is a simple eutectic type with a eutectic at 3.0 pct Si and 840°C. From the liquidus curve and with the aid of regular solution theory, the thermodynamic properties of the liquid Ag-Si system at 1420 °C have been determined. Silicon exhibits positive deviations from Raoultain behavior at all compositions, while silver exhibits both positive and negative deviations. MEASUREMENTS of silicon activities in liquid iron alloys by means of distribution studies between the immiscible liquids silver and iron have been reported by Chipman, Fulton, Gokcen, and caskey.&apos; The applicability of this technique is dependent, however, on the accuracy of the silicon activity values in the Ag-Si alloys, particularly in the dilute silicon region. Darken and Gurry2 have shown that log ?si/(1-xSi)2 is approximately linear with composition, but uncertainty exists in the extrapolation to dilute solutions. Their calculations are based on the old Ag-Si phase diagram of Arrivaut3 and any variation in the position of the liquidus curves will strongly influence the extrapolation. The purpose of this study is to redetermine the Ag-Si phase diagram and calculate the associated thermodynamic properties. EXPERIMENTAL The Ag-Si phase diagram was determined by thermal analysis of liquid alloys. The alloys were contained in a 35 mm alumina crucible under a protective stream of purified argon. The crucible was placed inside a 64 mm alumina tube fitted with a gas-tight, water-cooled, copper head. The tube and assembly were heated in a manually controlled globar furnace. The temperature was measured with a Pt, Pt + 10 pct Rh thermocouple in a high-temperature porcelain protection tube. The thermocouple calibration4 was checked against the melting point of pure silver at the start and during the course of the experiments, and against both gold and silver at the completion of the experiments. The alloys were prepared from granular silver analyzing 99.95 pct Ag and powdered silicon analyzing 99.88 pct Si and 0.026 pct Fe. Approximately 150 g of alloy were used for each run. The composition of the alloy was determined by withdrawing samples of the liquid alloy with a vycor tube-aspirator bulb device. Analysis of solidified samples agreed, for alloys containing less than 23 pct Si, within ±0.3 pct Si of the calculated composition. Duplicate samples showed a variance within 50.05 pct Si of the mean analysis. The alloy was heated to 100&apos; to 20pC above the estimated liquidus temperature and then the furnace was adjusted to give an average cooling rate of 2" to 7°C per min. A cooling curve was obtained by taking potentiometer readings at 15-sec intervals. Several analyses were made by recording the thermocouple output on a high-speed, Stip-chart recorder, with the exception of run NO. 11, a minimum of two thermal analyses were made for each alloy and the cooling curves then obtained duplicated the liquidus and eutectic temperatures to about 1°C. RESULTS The results of the thermal analysis are given in Table 1, and are represented as the Ag-Si phase dlagram, Fig. 1. The eutectic composition was found

Jan 1, 1963

By M. T. Simnad, C. E. Birchenall, M. H. Davis

The transport mechanisms previously proposed in wustite and hematite have been confirmed by movement of inert markers during the growth of these phases. By similar measurements the mechanism for magnetite has been determined. The rates of growth of multilayer scales on iron, magnetite and hematite on wustite, and hematite on magnetite have been measured. All rates are found to be diffusion controlled under the conditions of the experiments. MANY studies have been made of the rate of oxidation of iron in both the low temperature, film-forming region and the high temperature scaling range. The interpretation of the results has been greatly complicated by the formation of multi-layered scales containing the various phases of iron oxides. In most cases no attempt has been made to determine the composition of the scale and its dependence on time of oxidation in a quantitative manner. However, several recent studies&apos;" have taken this variable into account. It is generally agreed that the growth of thick scales on iron follows a parabolic rate law for the increase of total thickness. In the thin film region agreement has been claimed with parabolic equations of various forms and with logarithmic equations. The discussion here will be concerned only with the formation of scales of considerable thickness, greater than several microns, although some of the conclusions may be applicable to thin films. A brief survey will be given of the solid phases of the iron-oxygen system, the stability of wiistite in bulk and in thin films, the relative densities of iron in the metal and oxides, and the kinetics of forma- tion of oxide scales on iron. New experimental results will be introduced at several points during the discussion, and an attempt will be made to formulate a mechanistic picture consistent with these observations. The experimental techniques are described in an appendix. Iron-Oxygen System Fig. la shows the iron-oxygen phase diagram. Wüstite ("FeO"): The lowest of the oxides has a NaCl type cubic lattice formed by close-packing of the relatively large oxide ions with the smaller iron ions arranged in the interstices. The ionic radius for 0&apos; is about 1.3 A, while Fe++ has a radius of about 0.8A and Fe"&apos; about 0.7A. Its range of existence on the phase diagram is very wide for an ionic material of this type and does not seem to include the stoi-chiometric composition FeO. These deviations appear to be well established as vacancies on iron lattice sites by the comparison of lattice parameters and densities for a series of compositions by Jette and Foote.4 The limits of the field are disputed, but the work which seems most reliable" indicates vacancies in from 5 pct to more than 12 pct of the iron sites. In order for the crystal to be electrically neutral, there must be electron holes which correspond to the formation of trivalent iron ions equal to twice the number of vacancies. Magnetite ("Fe³O4"): Considerable disagreement also exists in the literature about the stable range of the Fe³O4 field. Some diagrams show the Fe³O4 composition to be lower in oxygen than the formula indicates, but Schenck6 gives a diagram from the

Jan 1, 1952

By Thomas L. Kesler

Present Raw Materials The lithium industry has had exceptional growth since publication of the last edition of this volume, and the present scale of mining and consumption of raw materials is a great many times that of 1949. The materials of present economic importance consist of four pegmatite minerals and lithium-bearing brine. Spodumene, a lithium pyroxene, occurs in greatest abundance, and is the chief source. It has the formula LiAlSi2O6 and theoretically may contain 8.03 pct Li2O, but in the more important deposits the content is 6.5 to 7.5 pct. The hardness is 6.5, the specific gravity 3.1 to 3.2, and the color mostly pale green to white although deep green, lilac, and yellow varieties exist. The crystals are prisms with strongly developed longitudinal cleavages, and crushing characteristically produces lath-shaped particles. Giant crystals up to 47 ft long are known, but in most occurrences the predominant size range is 0.5 to 12 in. long and 0.1 to 2 in. wide. Hypogene* alteration has formed lithia-bearing sericite and coarser muscovite and rarely eucryptite, while supergene* alteration yields kaolinite and hydrous mica. Lepidolite, of second importance, is a mica of varying composition approximating K2Li3-A14Si7O21(OH,F)3. It has lamellate cleavage, book structure, and a specific gravity of 2.8 to 3. The books range in size from microscopic to a diameter of several inches. The color is mostly violet, but other colors include pink, gray, yellow, and white. Most commercial lepidolite contains 3 to 4 pct Li20 and chemically is in the higher grade range of a series of lithium micas that includes polylithionite, zinnwaldite, and protolithionite. In this series, the content of Li2O is exceptionally as high as 7 pct. Petalite and amblygonite are also of economic importance, but are used in smaller amounts. Petalite has the formula LiA1Si4O10 and is white, gray, or pink. The hardness is 6, the specific gravity 2.4, the cleavage in two planes 114° apart, and the Li2O content commonly 3 to 4.7 pct with a maximum of 4.88. Amblygonite has the formula LiA1FPO4 in which OH may substitute for F to form montebrasite. It is white and has polysynthetic twinning in two directions at 90°. Amblygonite superficially resembles potash feldspar, but has a bluish or grayish tint unlike the cream or salmon tint of the feldspar.[t] The hardness is 6 and the specific gravity 3 to 3.1, and the content of Li2O is the highest among lithium minerals that occur in significant quantity, ranging mostly from 7.5 to 9 pct with a maximum of 10.2. The brine of Searles Lake in California30 has been a commercial source of lithium since 1938. See Chap. 7, p. 108. The "lake" is a saline evaporite deposit, and the exposed part has an area of 12 sq mi. To an average depth of 71 ft, this part of the deposit consists of crystalline salts with 50 pct interstitial voids. The voids are filled with brine that contains mainly sodium and potassium compounds, but the brine also contains 0.015 pct Li2O, which is recovered as dilithium sodium phosphate containing 21 pct Li20. This deposit overlies a

Jan 1, 1960

By P. Ramachandraraa, T. R. Anantharaman

THE technique developed by Duwez, Willens and Kle-ment&apos; for rapid solidification of molten alloys in small quantities by ejecting them on to a highly conducting substrate with the aid of a shock wave has come to be known as "liquid quenching" or "splat cooling" in literature and has already been applied to alloys of many binary systems.&apos; The very high cooling rates of the order of l060 to 1080 per sec obtained in this technique and the consequent drastic undercooling of the melt have led to such striking results as formation of new amorphous and crystalline metastable phases and extension of solid-solubility limits in many alloy systems. The cooling rates in these experiments can, however, be neither accurately measured nor effectively controlled and hence the occurrence of either more than one metastable phase or appreciable differences in constitution in splat-cooled alloys of the same composition cannot be ruled out.3 In fact, workers in two laboratories have reported formation of two different cubic metastable phases in liquid-quenched Au-Si alloys containing 17 to 20 at. pct si.4,5 The present note deals with some new and interesting results obtained in a Ag-21 at. pct Ge alloy and a Au-27 at. pct Ge alloy subjected to the liquid-quenching treatment at different cooling rates. Two alloys of nearly the same composition had earlier been rapidly solidified by the standard "gun technique" in the same laboratory and shown to solidify in nonequilibrium structures, viz., an hcp phase (a = 2.987Å;c =4.718Å) in the Ag-Ge system6,7 and both hcp (a = 2.885Å; c = 4.754Å) and tetragonal (a = 11.627A; c = 22.491Å) phases in the Au-Ge system.3 Apart from different substrates (copper and stainless steel), different melt temperatures (50º to 500°C above the liquidus), and different capillary sizes (0.4 to 1.5 mm diam) in the "gun technique", slower cooling rates of the order of l050C per sec were also obtained in the present work by replacing the substrate by water at room temperature in a modification of the technique due to Olsen and Hultgren.8 No attempt was made to measure the cooling rate in any experiment. The products varied from fine powder (>40 pct by wt—200 mesh) obtained by quenching in water to thin flakes and foils (11.0 sq mm to 4.0 sq cm) produced by splat cooling. They were subjected to the Debye-Scherrer method of X-ray examination in each case. In case of the Ag-Ge alloy, in addition to the expected metastable hcp phase,6 a coexistent tetragonal phase (a = 5.093,Å; c = 7.009Å) was detected in some experiments. Eight weak X-ray reflections from this phase could be identified, two of them being the same as reported earlier.7 With increase in the cooling rate, the dominant hcp phase seems to be first accompanied by traces of silver or germanium and then either homogeneous or mixed with traces of this new tetragonal phase. The splat-cooled Au-Ge alloy showed generally the expected hcp and tetragonal phases,3 but sometimes traces of germanium were also present. Further, two new tetragonal phases with the following lattice param ters could be clearly identified in samples quenched

Jan 1, 1970

By E. F. Sumner, C. K. Eilerts

A partial differential equation was developed and programmed to compute the cumulation and flow of the liquid phase of a gas-condensate fluid. It was found that such cumulation near the wellbore may attain saturations permitting liquid flow within periods of the order of 1 day. The radius at which this saturation obtains advances toward the external reservoir boundary with continued recovery, although it may move only 2 to 5 percent of that distance during the productive life of the well. This relatively high saturation can cause a serious dimunition in delivery capacity. The pressure dilferential required for flow of gas through a formation with such saturation may be as much as three times greater than the corresponding differential in a formation where saturation is less than 2 percent. Because of the radial geometry, total reservoir pressure differential required for flow with a zone of relatively high liquid saturation about the well was indicated to be two to three times greater than without the saturation. INTRODUCTION A computing program developed by the authors 1 to integrate the partial differential equation for transient radial flow of gas-condensate fluids required a prevalued function, W(Po) = kD(p0)/M(p0)z0(Po).......(1) related to cumulation of condensate in pores of the reservoir as pressure declines. Methods were available for relating mobility to saturation, saturation to liquid-vapor volume ratio, liquid-vapor volume ratio to pressure and, hence, mobility to pressure to obtain W(pD). However, certain assumptions had to be made in advance of program execution concerning movement of the liquid phase and change in radial distribution of liquid saturation as recovery progressed. Because reservoir fluid mobility and related pressure gradients are markedly dependent on liquid saturation, it was desirable to eliminate the necessity for these assumptions and in this respect improve the reliability of a result obtained by integration. Experimental research was begun to determine the relationship of variables that control the reservoir flow of low liquid-vapor ratio fluids. With the porous medium partly saturated, permeability to a two-phase flowing fluid could not be measured because the viscosity was unknown. Viscosity could not be measured without knowing permeability of the liquid-containing medium; but mobility, the ratio of permeability to viscosity, was measurable. This property, and liquid-vapor volume ratio of the flowing phases, have values determined by nature of the fluid and porous medium and, in addition, were found to be pressure, velocity and saturation dependent. A program developed by Kniazeff and Naville 2 for computing multicom-ponent, two-phase flow used polynomials to represent saturation dependence of permeabilities for gas and for liquid phases, and an effluent viscosity constant under reservoir conditions. The authors developed a program based on a partial differential equation of similar mass balance origin but designed to represent distribution of an unlimited number of components between gas and liquid phases utilizing the experimental information available as to variable dependence. Attention was given to liquid-vapor volume ratio of the flowing phases, a property which is essential as a liquid saturation boundary condition. A program for computing implicitly saturation increase at uniform intervals along the drainage radius was combined with an existing program for calculating pressures, and the two were used alternately in an iterative solution for both saturations and pressures. The function W(pD) needed for calculating pressures was replaced by the ratio of mobility to compressibility factor. BASIC EQUATIONS The partial differential equation for calculating

By J. Buchwald, R. W. Heckel

THE DeHoff method&apos; of analysis of ellipsoids of constant shape provides a quantitative metallo-graphic technique whereby the actual size distribution of the ellipsoids may be determined from polished and etched random planar sections. This method provides a useful metallographic tool since it appears to be the only method available for determining the size distribution of nonequiaxed second-phase particles. This method, however, assumes that the type of particle being studied is known to be either oblate or prolate of a fixed minor to major axis ratio, q. This, in general, means that one assumes either oblate or prolate ellipsoids of a given q and checks the total volume and surface area of the second phase as determined from the particle size distribution to values of these quantities determined by other techniques. Suitable check methods may be point counting, lineal fraction, and areal fraction methods for obtaining the total volume and the Smith and Guttman2 method of intercepts for obtaining the total surface area. If the initial guess at particle shape and q were incorrect, i.c., the volume and surface information obtained from the particle size distribution data does not agree with those values obtained by other techniques, another assumption must be made and the particle size dist distribution must be recalculated. A current study in this laboratory has involved a large number of these calculations. To facilitate the handling of the calculations, the DeHoff method was programmed in the FORTRAN language for an IBM 1620 computer. The purpose of this note is to briefly describe this program. The complete program along with a list of variable names, a sample input, and a sample output may be obtained from the senior author. Basically, the program provides for the calculation of particle size distributions for a series of q values for both oblate and prolate ellipsoids for each set of input data. The total volume of second-phase particles per unit volume are calculated for each calculated particle size distribution. The output of the program is arranged to allow a rapid comparison of the calculated volume and surface values to data obtained by independent check measurements. A condensed flow chart of the program in the notation of DeHoff1 is given in Fig. 1 The calculation of the number of particles per unit volume in the jth size class, Ni, according to the DeHoff method&apos; is: where k(q) is the shape-correction factor given by DeHoff as a function of q for both oblate and prolate ellipsoids, A is the size-class increment, k is the number of size classes, ni is the number of particles in the ith class on the planar measurement surface, and B(j,i) are the saltykov3 coefficients which correct for measurement surfaces which do not pass through the major and minor axes of the particles. The values of /3(j,i) are included as a two-dimensional array in the program. Particular values of k(q) are included in the program in increments of q of 0.05. The first calculation is carried out for q = 1 (spheres), the second for q = 0.95 oblate, the third for q = 0.95 prolate, and so forth. The number of q values chosen for the calculation is determined by a control card in the input for each set of data.

Jan 1, 1965